Differentiation

[andreipanait]

I'm reading through my text book and the term differentiate is very vaguely explained. For example theres a question where you're given and function and it says to differentiate it with respect to x. I'm confused as to what they are asking really, do they want us to find the derivative of the function? and how would you go about differentiating. The function is f(x)= (x^2 + 1)(3x)(x+7) . Oh and also what is the difference between implicit differentiation and just differentiation?
Thank you

 

[galactus]

Exapnding out the function you get:

\(\displaystyle f(x)=3x^{4}+21x^{3}+3x^{2}+21x\)

\(\displaystyle f'(x)=12x^{3}+63x^{2}+6x+21\)

The principles behind differentiation are beyond the scope of this forum. There are many a book and online sites to answer your questions.

Try Karl'sCalculus.com

 

[tkhunny]

Yes.
Find it using whatever methods are available to you.
The other is explicit.

Seriously, ...

"To Differentiate", in this context, is to find the derivative, or to calculate it. "with respect to" defines the variable of interest -- all others being assumed to be constant.

You should have learned a few rules about how to find derivatives. Power Rule, Product Rule, Chain Rule, etc.

"implicit" is really rather clear in its intent. Rather than calculating the derivative directly, you must sneak around a little. y = x+2 has an explicit expression for 'y' and the derivative of 'y' with respect to 'x' can be calculated explicitly. x^2 + 3xy + 4y^2 + 5x + 6y - 7 = 0 is substantially more difficult to express explicitly as y = f(x).

Okay, that's a lovely textbook section outline. Now, let's do some book reading, some listening in class, and see if you can solve a few problems on your own. If you get stuck, present one or two here, showing your work. Someone will be pleased to assist.

 

[andreipanait]

thanks a lot